10 tips on how to improve your math skills, common core math example
Calculators can be surprisingly useful, but they are not always at hand. In addition, not everyone is comfortable getting their calculators or phones to calculate how much to pay at a restaurant or to calculate the size of the tip. Here are ten tips that can help you do all these calculations in your mind. It’s actually not hard at all, especially if you remember a few simple rules.
Add and subtract from left to right.
Remember when they taught us in school to add and subtract from the right to left column? This addition and subtraction is convenient when you have a pencil and a piece of paper at hand, but in your mind these mathematical actions are easier to do, counting from left to right. Among the left there is a number that defines big values, for example, hundreds and dozens, and on the right there are smaller ones, that is units. From left to right, it is more intuitive to count. Thus, adding 58 and 26, start with the first digits, first 50 + 20 = 70, then 8 + 6 = 14, then add both results – and you get 84. Easy and simple.
Make it easy for yourself.
If you encounter a complex example or task, try to find a way to simplify it, for example by adding or subtracting a certain number to make the overall calculation easier. If, for example, you need to calculate how much 593 + 680 would be, first add 7 to 593 to get a more convenient number 600. Calculate what would be 600 + 680, and then take the same 7 from the result 1280 to get the correct answer – 1273.
You can do the same with multiplication. To multiply 89 x 6, calculate how many would be 90 x 6, and then subtract the remaining 1 x 6. Thus, 540 – 6 = 534.
Remember the standard blocks
Memorizing the multiplication tables is an important and necessary part of mathematics, which perfectly helps to solve examples in the mind.
By memorizing basic “standard blocks” of common core math example, such as multiplication tables, square roots, percentage ratios of decimal and common shot, we can immediately get answers to simple problems hidden in more difficult ones.
Remember the useful tricks
To cope with multiplication faster, it is important to remember a few simple tricks. One of the most obvious rules is to multiply by 10, i.e. simply adding zero to the number to be multiplied or moving a comma to one decimal place. When multiplied by 5, the answer will always end with 0 or 5.
Also, by multiplying the number by 12, first multiply it by 10 and then by 2, then add the results. For example, when calculating 12 x 4, first multiply 4 x 10 = 40 and then 4 x 2 = 8, and add 40 + 8 = 48. By multiplying by 15, just multiply the number by 10, and then add another half of the result, for example, 4 x 15 = 4 x 10 = 40, plus another half (20), you get 60.
There is also a tricky trick to multiply by 16. First, multiply the number in question by 10 and then multiply half the number by 10. After that, add both results to the number to get the final answer. So to calculate 16 x 24, first calculate 10 x 24 = 240, then half 24, that is 12, multiply by 10 and you get 120. And the last step: 240 + 120 + 24 = 384.
Common core math example the squares and their roots.The squares and their roots are very useful.
Almost like a multiplication table. And they can help with multiplication of larger numbers. The square is obtained by multiplying the number by itself. That’s how multiplication with squares works.
Let’s assume for a moment that we don’t know the answer by 10 x 4. First, we find out the average number between these two numbers, which is 7 (i.e. 10 – 3 = 7, and 4 + 3 = 7, with the difference between the average number being 3 – this is important).
Then we define square 7, which equals 49. We now have a number close to the final answer, but it is not close enough. To get the correct answer, we return to the difference between the mean number (in this case 3), its square gives us 9. The last step involves a simple subtraction, 49 – 9 = 40, you now have the correct answer.
This is like a roundabout and too complicated way to calculate how much 10 x 4 will be, but the same technique works fine for large numbers as well. Take, for example, 15 x 11. First we have to find the average number between these two (15 – 2 = 13, 11 + 2 = 13). Square 13 is 169. The square of difference between the average number 2 is 4. We get 169 – 4 = 165, that’s the correct answer.
Sometimes an approximate answer is enough.
If you are trying to solve complex problems in your mind, it is not surprising that it takes a lot of time and effort. If you do not need an absolutely accurate answer, it may be sufficient to calculate an approximate number.
The same is true for tasks in which you do not know all the exact data. For example, during the Manhattan Project, physicist Enrico Fermi wanted to roughly calculate the force of an atomic explosion before scientists could get accurate data. To that end, he threw paper scraps on the floor and watched them from a safe distance as the blast wave reached the paper. Measuring the distance the scraps moved, he assumed that the blast force was approximately 10 kilotons of TNT equivalent. This estimate was accurate enough to suggest overtones.
Fortunately, we don’t have to regularly estimate the approximate atomic blast force, but approximate estimates wouldn’t hurt if you had to assume, for example, how many piano tuners are in town. The easiest way to do that is to operate with numbers that are simply divided and multiplied. So, first you estimate the population of your city (for example, one hundred thousand people), then you estimate the estimated number of pianos (say, ten thousand), and then the number of piano tuners (for example, 100). You won’t get an exact answer, but you will be able to quickly estimate the approximate number of pianos.
Rearrange the examples
Basic rules of 1st grade math worksheets help to reconstruct complex examples into simpler ones. For example, calculating a 5 x (14 + 43) example in your mind seems like a huge and even impossible task, but the example can be “broken” into three rather simple calculations. For example, this impossible task can be rebuilt in the following way: (5 x 14) + (5 x 40) + (5 x 3) = 285. It’s not that difficult, is it?
Simplify the tasks.
If the task seems difficult, simplify it. It is always easier to deal with several simple tasks than with one complicated one. The solution to many complex examples in your mind is the ability to correctly divide them into simpler examples that are easy to solve.
For example, multiplying by 8 is easiest, doubling the number three times. So, instead of trying to decide how many would be 12 x 8 in the traditional way, just double the number 12 times three: 12 x 2 = 24, 24 x 2 = 48, 48 x 2 = 96.
Or multiply by 5, first multiply by 10 as it is easy, then divide the result by 2 as it is also quite easy. For example, for a 5 x 18 solution, calculate 10 x 18 and divide by 2, where 180 : 2 = 90.